Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110} \displaystyle \lim_{x \to +\infty}\left ( \frac{2x}{x^2+1}+\frac{3x-1}{x+5} \right )$ is gelijk aan	A. 1
	B.
	C. 3
	D. 0
	E. 5

[ 5-6970 - op net sinds 17.7.15-(E)-18.11.2024 ]

Translation in E N G L I S H

$\displaystyle \lim_{x \to \infty}\left ( \frac{2x}{x^2+1}+\frac{3x-1}{x+5} \right )$ is equal to	A. 1
	B. ∞
	C. 3
	D. 0
	E. 5

Oplossing - Solution

$\\\displaystyle\lim_{x\to+\infty}\left(\frac{2x}{x^2+1}+\frac{3x-1}{x+5}\right)=\displaystyle\lim_{x\to+\infty}\frac{2x}{x^2+1}+\displaystyle\lim_{x\to+\infty}\frac{3x-1}{x+5}\\=\displaystyle\lim_{x\to+\infty}\frac{2x}{x^2}+\displaystyle\lim_{x\to+\infty}\frac{3x}{x}=\displaystyle\lim_{x\to+\infty}\frac2x+\displaystyle\lim_{x\to+\infty}3=0+3=3$